\(यदि (U={1,2,\ldots,54}), (A={x:x\) 6 से विभाज्य है\(}) और (B={x:x\) 9 से विभाज्य है\(}), तो (|A'\cup B'|) कितना है\)?
\(If (U={1,2,\ldots,54}), (A={x:x\) is divisible by \(6}) and (B={x:x\) is divisible by \(9}), what is (|A'\cup B'|)\)?
Explanation opens after your attempt
Correct Answer
C. (51)
Concept
By De Morgan's law, (A'\cup B'=\(A\cap B\)'). \(A\cap B\) has (3) multiples of (18), so \(|A'\cup B'|=54-3=51\).
Why this answer is correct
The correct answer is C. (51). By De Morgan's law, (A'\cup B'=\(A\cap B\)'). \(A\cap B\) has (3) multiples of (18), so \(|A'\cup B'|=54-3=51\).
Exam Tip
डी मॉर्गन नियम से (A'\cup B'=\(A\cap B\)') है। \(A\cap B\) में (18) के (3) गुणज हैं, इसलिए \(|A'\cup B'|=54-3=51\)।
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